Programs in Physics & Physical Chemistry
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|Manuscript Title: CheMPS2: a free open-source spin-adapted implementation of the density matrix renormalization group for ab initio quantum chemistry|
|Authors: Sebastian Wouters, Ward Poelmans, Paul W. Ayers, Dimitri Van Neck|
|Program title: CheMPS2|
|Catalogue identifier: AESE_v1_0|
Distribution format: tar.gz
|Journal reference: Comput. Phys. Commun. 185(2014)1501|
|Programming language: C++.|
|Operating system: Scientific Linux 6.0.|
|RAM: 10 MB - 64 GB|
|Keywords: Density matrix renormalization group, Matrix product state, SU(2) Spin symmetry, Abelian point group symmetry, ab initio quantum chemistry.|
|PACS: 31.15.ae, 31.15.vj, 31.50.Df.|
External routines: Basic Linear Algebra Subprograms (BLAS), Linear Algebra Package (LAPACK), GNU Scientific Library (GSL), and Hierarchical Data Format Release 5 (HDF5)
Nature of problem:
The many-body Hilbert space grows exponentially with the number of single-particle states. Exact diagonalization solvers can therefore only handle small systems, of up to 18 electrons in 18 orbitals. Interesting active spaces are often significantly larger.
The density matrix renormalization group allows the extension of the size of active spaces, for which numerically exact solutions can be found, to about 40 electrons in 40 orbitals. In addition, it provides a rigorous variational upper bound to energies, as it has an underlying wavefunction ansatz, the matrix product state.
Our implementation of the density matrix renormalization group is spin-adapted. This means that targeted eigenstates in the active space are exact eigenstates of the total electronic spin operator. Hamiltonians which break this symmetry (a magnetic field term for example) cannot be handled by our code. As electron repulsion integrals in gaussian basis sets have eightfold permutation symmetry, we have used this property in our code.
The nature of the matrix product state ansatz allows for exact spin coupling. In CheMPS2, the total electronic spin is imposed (not just the spin projection), in addition to the particle-number and abelian point-group symmetries.
The running time depends on the size of the targeted active space, the number of desired eigenstates, their symmetry, the density of states, the individual orbital symmetries, the orbital ordering, the desired level of convergence, and the chosen convergence scheme. To converge a single point of one of the dissociation curves of the carbon dimer (D∞h → D2h symmetry) in the cc-pVDZ basis (28 orbitals; their ordering is described in section 5.3) with 2500 reduced renormalized basis states (see the convergence scheme in section 5.4; the variational energy then lies 0.1 mEh above the fully converged result) takes about 8 hours on a single node with a dual-socket octa-core Intel Xeon Sandy Bridge (E5-2670) (16 cores at 2.6 GHz), and requires 6 GB of RAM.
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